We develop a quantitative model for adenovirus replication. The model makes three astonishing predictions: the rate of displacement synthesis exceeds the rate of complementary synthesis, the rate of initiation is very low, and the doubling time to produce mature molecules is significantly longer than the average time to synthesize a single strand. We show how to measure the rates of replication and initiation using electron microscopy. We propose a novel route leading to the production of defective adenovirus genomes. We give evidence for the smallest defective adenovirus genome yet reported: a molecule 445 base pairs in size. We use a remarkable filter-binding assay specific for the adenovirus covalent terminal protein-DNA complex to study the role and synthesis of the terminal protein during infection. Experiments are described to test whether the terminal protein acts as a primer for DNA synthesis.